Bikes. Although [humans are not as smart as horses when it comes to not crashing against each other](https://worldbuilding.stackexchange.com/a/136772/21222), bikes are cheaper to acquire and maintain, and will generally keep the streets clearer. Drivers can benefit from the exercise.

Also, this being about Britain, I had a certain song from Queen on my mind while typing this.

> Bicycle races are coming your way  
So forget all your duties oh yeah!  
Fat bottomed girls they'll be riding today  
So look out for those beauties oh yeah

Edit to address this comment from Julian Egner:

> This would a great answer if all drivers would have to use the same transpotation type - but it is no so good if all the others use big cars and you are on your bike. even with all the traffic laws it is sometimes not easy to avoid crashes, which would not end well for the biker.

Biked can navigate parks, squares, people's backyards, sidewalks, shopping malls, food courts, piers, subway platforms etc. with more ease than cars<sup>citation needed</sup>. Just stick to where it's safe.